The new cultivar originated as a limb sport mutation of a ‘Nagafu-6’ (unpatented) Fuji apple tree. It was discovered by the inventor in 1994 in a cultivated orchard at Totara Grove Orchard, New Zealand. ‘CABp Fuji’ was asexually propagated at Totara Grove Orchard in 1995, and has been shown to remain true to type over successive generations.